Let the number of apples you currently have be denoted by $x$, and the number of apples I currently have be denoted by $y$.

We are given two conditions:

1. If I give you seven apples, then you will have five times as many apples as I would have. This translates to the equation: $y - 7 = 5(x + 7)$ (After giving you 7 apples, I have $y - 7$ apples, and you have $x + 7$ apples.)

2. If you give me seven apples, we will both have the same number of apples. This translates to the equation: $x - 7 = y + 7$ (After giving me 7 apples, you have $x - 7$ apples, and I have $y + 7$ apples.)

Step 1: Solve the second equation

From the second equation: $x - 7 = y + 7$ Simplify it: $x = y + 14$

Step 2: Substitute into the first equation

Now, substitute $x = y + 14$ into the first equation: $y - 7 = 5((y + 14) + 7)$ Simplify the right-hand side: $y - 7 = 5(y + 21)$ Distribute the 5 on the right: $y - 7 = 5y + 105$ Now, move all terms involving $y$ to one side and constant terms to the other: $y - 5y = 105 + 7$ $-4y = 112$ Solve for $y$: $y = \frac{112}{-4} = -28$

Step 3: Solve for $x$

Now that we know $y = -28$, substitute this back into the equation $x = y + 14$: $x = -28 + 14 = -14$

Final Answer:

You currently have -14 apples, and I currently have -28 apples.

These negative values imply that both of us owe apples to each other, which could represent a situation of debt.

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Would you like me to elaborate on any step, or do you have more questions about this problem?

Here are some related questions for further exploration:

1. How can negative numbers be applied in real-world scenarios like debts or credits?
2. How does algebraic substitution work in solving systems of equations?
3. What are some alternative ways to represent debts in mathematical problems?
4. How would the problem change if the relationship between the apples was not linear (i.e., not a multiple of 5)?
5. What other types of word problems are commonly modeled by systems of equations?

Tip: When solving word problems, it's helpful to define variables clearly and translate the statements into algebraic equations step by step.